I am an electrical engineer for a moderately large company.
My work is quite challenging and usually I am at work for 10 hours per day, sometimes more. The real question here is: how do you define "productivity"?
It is easier to quantify when dealing with such things as factory or production work: in those cases, the goal is to produce A Thingy every X number of minutes. When it comes to the design and development side of engineering, the value of time spent cannot be quantified in the same manner as it can for more assembly-line type situations where tasks and outcomes are clearly defined and standardized.
Much of the work I do requires thought. If I am examining a particular design for electromagnetic compatability, or attempting to discern the operation of a particular system by looking at the schematic, etc., I cannot simply stare at various pieces of paper and hope to absorb the necessary information by osmosis. In order to really learn something, or design something, I need to examine an idea or product description and process the information I receive. Processing does not occur instantaneously. Perhaps it does for some lucky few, but despite my ability to come to eventual deep understanding of various electronic devices and concepts, my processing speed is at the mercy of the way my brain works.
Sometimes, the best way to figure out how something works (or design a way to make it work better) is to step back and let the information you have taken in over the past few hours settle and shift in your mind. I try to stay off the Internet while working but I will not say I spend 10 hours every day doing absolutely nothing but observable "work". Sometimes it is necessary to pause and let ideas mingle and process them without putting pressure on yourself to come to an immediate solution or conclusion.
There have been times when I've spent hours staring at a piece of code, trying different tactics to get it to work, and coming up with nothing. Sometimes I will think of the solution after only a few minutes of "Internet break time": while reading an article about cryonics or neuroscience or something else that is interesting to me but not necessarily work-related. If I was not reading these articles I would just be staring into space, so I figure that the time is well spent as long as I produce something for my employers in a timely manner.
It is similar to the situation in which "sleeping on" a decision results in a more satisfying solution. Allowing the brain to put the problem on its background-processing circuits is often a very important and valid tactic for solving complex problems. If I never read articles online at all I would most certainly be a less productive, unhappier employee and I don't think my bosses want that.
And in case anyone is wondering, I am not posting this from work. I generally try to reserve longer comments for the home environment.